矩阵分解和矩阵方程AX=B，AXB=C的解

矩阵分解和矩阵方程AX=B，AXB=C的解

摘要

本文详细地阐述了矩阵的QR分解，奇异值分解，利用这些矩阵分解，给出了矩阵方程AX=B， AXB=C有解条件及有解时解的1般表达式。

关键词：初等变换；QR分解；奇异值分解；矩阵方程。

Matrix Decomposition and the Solutions of the Matrix Equations AX=B,AXB=C

Abstract

In t€his pape♪r, the QR decomposition, Singular Value decomposition of matrix have been remarked in detail.

Using these matrix decompositions, the necessary and sufficient conditionsน of the matrix equations AX=B and

AXB=C have a solution and have an unique solution are given. And when the matrix equations have a Solution or have an unique solution, the expressio ﭢn of the solution has been presented.

Key Words: Fundamental transformation; QR decomposition; Singular value decomposition; ☯matrix equation.